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International Journal of Antennas and Propagation
Volume 2015, Article ID 165935, 14 pages
Research Article

Multiantenna Spectrum Sensing in the Presence of Multiple Primary Users over Fading and Nonfading Channels

National Institute of Telecommunications (INATEL), P.O. Box 05, 37540-000 Santa Rita do Sapucaí, MG, Brazil

Received 19 February 2015; Accepted 25 April 2015

Academic Editor: Song Guo

Copyright © 2015 Dayan Adionel Guimarães et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The basis of this paper is Wei and Tirkkonen, 2012, in which expressions for the key performance metrics of the sphericity test applied to the multiantenna cooperative spectrum sensing of multiple primary transmitters in cognitive radio networks over nonfading channels are provided. The false alarm and the detection probabilities were derived in Wei and Tirkkonen, 2012, based on approximations obtained by matching the moments of the test statistics to the Beta distribution. In this paper we show that the model adopted in Wei and Tirkkonen, 2012, does not apply directly to fading channels, yet being considerably inaccurate for some system parameters and channel conditions. Nevertheless, we show that the original expressions from Wei and Tirkkonen, 2012, can be simply and accurately applied to a modified model that considers fixed or time-varying channels with any fading statistic. We also analyze the performance of the sphericity test and other competing detectors with a varying number of primary transmitters, considering different situations in terms of the channel gains and channel dynamics. Based on our results, we correct several interpretations from Wei and Tirkkonen, 2012, in what concerns the performance of the detectors, both over a fixed-gain additive white Gaussian noise channel and over a time-varying Rayleigh fading channel.